What a lovely hat

We consider the problem of electing a leader among $n$ parties with the guarantee that each (honest) party has a reasonable probability of being elected, even in the presence of a coalition that controls a subset of parties, trying to bias the output. This notion is called ``game-theoretic fairness'' because such protocols ensure that following the honest behavior is an equilibrium and also the best response for every party and coalition. In the two-party case, Blum's commit-and-reveal...

State-of-the-art garbling schemes for boolean circuits roughly consist of two families, i.e., ideal model garbling that combines linear operations and ideal blockciphers (aiming at maximizing performance), and PRF-based garbling that insists on using theoretically sound assumptions. In the linear garbling framework introduced by Zahur, Rosulek, and Evans (Eurocrypt 2015), it was established that garbling an AND gate requires at least $2(\kappa +1)$ bits of ciphertext, with $\kappa$ as the...

We initiate the study of the black-box complexity of private-key functional encryption (FE). Of central importance in the private-key setting is the inner-product functionality, which is currently only known from assumptions that imply public-key encryption, such as Decisional Diffie-Hellman or Learning-with-Errors. As our main result, we rule out black-box constructions of private-key inner-product FE from random oracles. This implies a black-box separation between private-key...

We extend the concept of access control for functional encryption, introduced by Abdalla et al. (ASIACRYPT 2020), to function-revealing encryption (Joy and Passelègue, SCN 2018). Here “access control” means that function evaluation is only possible when a specified access policy is met. Specifically, we introduce access-controlled inner product function-revealing encryption (AC-IPFRE) and give two applications. On the theoretical side, we use AC-IPFRE to show that function-hiding...

This paper partly solves the open problem of tight trade-off of client storage and server time in the client preprocessing setting of private information retrieval (PIR). In the client preprocessing setting of PIR, the client is allowed to store some hints generated from the database in a preprocessing phase and use the hints to assist online queries. We construct a new single-server client preprocessing PIR scheme. For a database with $n$ entries of size $w$, our protocol uses $S=O((n/T)...

For a finite field $\mathbb{F}$ of size $n$, the (patched) inverse permutation $\operatorname{INV}: \mathbb{F} \to \mathbb{F}$ computes the inverse of $x$ over $\mathbb{F}$ when $x\neq 0$ and outputs $0$ when $x=0$, and the $\operatorname{ARK}_K$ (for AddRoundKey) permutation adds a fixed constant $K$ to its input, i.e., $$\operatorname{INV}(x) = x^{n-2} \hspace{.1in} \mbox{and} \hspace{.1in} \operatorname{ARK}_K(x) = x + K \;.$$ We study the process of alternately applying the...

In this paper, we study multi-party non-interactive key exchange (NIKE) in the fine-grained setting. More precisely, we propose three multi-party NIKE schemes in three computation models, namely, the bounded parallel-time, bounded time, and bounded storage models. Their security is based on a very mild assumption (e.g., NC1 ⊊ ⊕L/poly) or even without any complexity assumption. This improves the recent work of Afshar, Couteau, Mahmoody, and Sadeghi (EUROCRYPT 2023) that requires idealized...

In this paper, we study the requirement for quantum random access memory (QRAM) in quantum lattice sieving, a fundamental algorithm for lattice-based cryptanalysis. First, we obtain a lower bound on the cost of quantum lattice sieving with a bounded size QRAM. We do so in a new query model encompassing a wide range of lattice sieving algorithms similar to those in the classical sieving lower bound by Kirshanova and Laarhoven [CRYPTO 21]. This implies that, under reasonable assumptions,...

Deterministic broadcast protocols among $n$ parties tolerating $t$ corruptions require $\min\{f+2, t+1\}$ rounds, where $f \le t$ is the actual number of corruptions in an execution of the protocol. We provide the first protocol which is optimally resilient, adaptively secure, and asymptotically matches this lower bound for any $t<(1-\varepsilon)n$. By contrast, the best known algorithm in this regime by Loss and Nielsen (EUROCRYPT'24) always requires $O(\min\{f^2, t\})$ rounds. Our main...

A trapdoor Memory-Hard Function is a function that is memory-hard to evaluate for any party who does not have a trapdoor, but is substantially less expensive to evaluate with the trapdoor. Biryukov and Perin (ASIACRYPT 2017) introduced the first candidate trapdoor Memory-Hard Function called Diodon which modifies a Memory-Hard Function called Scrypt by replacing a hash chain with repeated squaring modulo a composite number $N=pq$. The trapdoor, which consists of the prime factors $p$ and...

The $k$-Tree algorithm [Wagner 02] is a non-trivial algorithm for the average-case $k$-SUM problem that has found widespread use in cryptanalysis. Its input consists of $k$ lists, each containing $n$ integers from a range of size $m$. Wagner's original heuristic analysis suggested that this algorithm succeeds with constant probability if $n \approx m^{1/(\log{k}+1)}$, and that in this case it runs in time $O(kn)$. Subsequent rigorous analysis of the algorithm [Lyubashevsky 05, Shallue 08,...

We consider 3 related cryptographic primitives, private information retrieval (PIR) protocols, conditional disclosure of secrets (CDS) protocols, and secret-sharing schemes; these primitives have many applications in cryptography. We study these primitives requiring information-theoretic security. The complexity of these primitives has been dramatically improved in the last few years are they are closely related, i.e., the the 2-server PIR protocol of Dvir and Gopi (J. ACM 2016) was...

At Eurocrypt 2015, Zahur, Rosulek, and Evans proposed the model of Linear Garbling Schemes. This model proved a $2\kappa$-bit lower bound of ciphertexts for a broad class of garbling schemes. Since then, several methods have been developed that bypass this lower bound, albeit with a notable limitation: Their reliance on specifically correlated input wire labels restricts their applicability across most gates. At Crypto 2021, Rosulek and Roy presented the innovative "three-halves" garbling...

We consider indistinguishability obfuscation (iO) for multi-output circuits $C:\{0,1\}^n\to\{0,1\}^n$ of size s, where s is the number of AND/OR/NOT gates in C. Under the worst-case assumption that NP $\nsubseteq$ BPP, we establish that there is no efficient indistinguishability obfuscation scheme that outputs circuits of size $s + o(s/ \log s)$. In other words, to be secure, an efficient iO scheme must incur an $\Omega(s/ \log s)$ additive overhead in the size of the obfuscated circuit. The...

It is well known that estimating a sharp lower bound on the second-order nonlinearity of a general class of cubic Booleanfunction is a difficult task. In this paper for a given integer $n \geq 4$, some values of $s$ and $t$ are determined for which cubic monomial Boolean functions of the form $h_{\mu}(x)=Tr( \mu x^{2^s+2^t+1})$ $(n>s>t \geq 1)$ possess good lower bounds on their second-order nonlinearity. The obtained functions are worth considering for securing symmetric...

The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks---that is, adversarial subversion---of the component round functions. Specifically, we establish that a Feistel-based construction with more than $337n/\log(1/\epsilon)$ rounds can transform a subverted random function---which disagrees with the original one at a small...

Forward-Secure Key-Encapsulation Mechanism (FS-KEM; Canetti et al. Eurocrypt 2003) allows Alice to encapsulate a key $k$ to Bob for some time $t$ such that Bob can decapsulate it at any time $t'\leq t$. Crucially, a corruption of Bob's secret key after time $t$ does not reveal $k$. In this work, we generalize and extend this idea by also taking Post-Compromise Security (PCS) into account and call it Interval Key-Encapsulation Mechanism (IKEM). Thus, we do not only protect confidentiality...

Merkle trees play a crucial role in blockchain networks in organizing network state. They allow proving a particular value of an entry in the state to a node that maintains only the root of the Merkle trees, a hash-based signature computed over the data in a hierarchical manner. Verification of particular state entries is crucial in reaching a consensus on the execution of a block where state information is required in the processing of its transactions. For instance, a payment transaction...

Sigma protocols are elegant cryptographic proofs that have become a cornerstone of modern cryptography. A notable example is Schnorr's protocol, a zero-knowledge proof-of-knowledge of a discrete logarithm. Despite extensive research, the security of Schnorr's protocol in the standard model is not fully understood. In this paper we study Kilian's protocol, an influential public-coin interactive protocol that, while not a sigma protocol, shares striking similarities with sigma protocols....

We present novel Secure Multi-Party Computation (SMPC) protocols to perform Breadth-First-Searches (BFSs) and determine maximal flows on dense secret-shared graphs. In particular, we introduce a novel BFS protocol that requires only $\mathcal{O}(\log n)$ communication rounds on graphs with $n$ nodes, which is a big step from prior work that requires $\mathcal{O}(n \log n)$ rounds. This BFS protocol is then used in a maximal flow protocol based on the Edmonds-Karp algorithm, which requires...

Recently, there has been a lot of interest in improving the understanding of the practical hardness of the 3-Tensor Isomorphism (3-TI) problem, which, given two 3-tensors, asks for an isometry between the two. The current state-of-the-art for solving this problem is the algebraic algorithm of Ran et al. '23 and the graph-theoretic algorithm of Narayanan et al. '24 that have both slightly reduced the security of the signature schemes MEDS and ALTEQ, based on variants of the 3-TI problem...

The Doubly-Efficient Private Information Retrieval (DEPIR) protocol of Lin, Mook, and Wichs (STOC'23) relies on a Homomorphic Encryption (HE) scheme that is algebraic, i.e., whose ciphertext space has a ring structure that matches the homomorphic operations. While early HE schemes had this property, modern schemes introduced techniques to manage noise growth. This made the resulting schemes much more efficient, but also destroyed the algebraic property. In this work, we study algebraic HE...

Functional Encryption (FE) is a powerful notion of encryption which enables computations and partial message recovery of encrypted data. In FE, each decryption key is associated with a function $f$ such that decryption recovers the function evaluation $f(m)$ from an encryption of $m$. Informally, security states that a user with access to function keys $\mathsf{sk}_{f_1}, \mathsf{sk}_{f_2}, \ldots$ (and so on) can only learn $f_1(m), f_2(m), \ldots$ (and so on) but nothing more about the...

In this paper, we formulate a special class of systems of linear equations over finite fields that appears naturally in the provable security analysis of several MAC and PRF modes of operation. We derive lower bounds on the number of solutions for such systems adhering to some predefined restrictions, and apply these lower bounds to derive tight PRF security for several constructions. We show security up to $2^{3n/4}$ queries for the single-keyed variant of the Double-block Hash-then-Sum...

We propose a generalization of Zhandry’s compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability of an algorithm for any predicate on input-output pairs, a key feature of Zhandry’s technique that had hitherto resisted attempts at generalization to random permutations. One key technical ingredient is to use strictly monotone factorizations to...

We address the black-box complexity of constructing pseudorandom functions (PRF) from pseudorandom generators (PRG). The celebrated GGM construction of Goldreich, Goldwasser, and Micali (Crypto 1984) provides such a construction, which (even when combined with Levin's domain-extension trick) has super-logarithmic depth. Despite many years and much effort, this remains essentially the best construction we have to date. On the negative side, one step is provided by the work of Miles and Viola...

(Receiver) Anamorphic encryption, introduced by Persiano $ \textit{et al.}$ at Eurocrypt 2022, considers the question of achieving private communication in a world where secret decryption keys are under the control of a dictator. The challenge here is to be able to establish a secret communication channel to exchange covert (i.e. anamorphic) messages on top of some already deployed public key encryption scheme. Over the last few years several works addressed this challenge by showing...

In this work we prove lower bounds on the (communication) cost of maintaining a shared key among a dynamic group of users. Being "dynamic'' means one can add and remove users from the group. This captures important protocols like multicast encryption (ME) and continuous group-key agreement (CGKA), which is the primitive underlying many group messaging applications. We prove our bounds in a combinatorial setting where the state of the protocol progresses in rounds. The state of the...

The collision-resistant hash function is an early cryptographic primitive that finds extensive use in various applications. Remarkably, the Merkle-Damgård and Merkle tree hash structures possess the collision-resistance preserving property, meaning the hash function remains collision-resistant when the underlying compression function is collision-resistant. This raises the intriguing question of whether reducing the number of underlying compression function calls with the...

Randomized distributed function computation refers to remote function computation where transmitters send data to receivers which compute function outputs that are randomized functions of the inputs. We study the applications of semantic communications in randomized distributed function computation to illustrate significant reductions in the communication load, with a particular focus on privacy. The semantic communication framework leverages generalized remote source coding methods, where...

A sequential function is, informally speaking, a function $f$ for which a massively parallel adversary cannot compute "substantially" faster than an honest user with limited parallel computation power. Sequential functions form the backbone of many primitives that are extensively used in blockchains such as verifiable delay functions (VDFs) and time-lock puzzles. Despite this widespread practical use, there has been little work studying the complexity or theory of sequential...

Building on the recently proposed LWR-based threshold-PRF LaKey, we propose two new constructions. First, we propose an optimized threshold-PRF with significantly reduced round and communication complexity. We achieve this by improving the underlying bit truncation protocol, as well as the lower bound on the required number of LWR instances. Second, we show that the same underlying PRF construction lends itself as a basis for a novel and efficient exponent-VRF. We implement prototypes of...

We study network-agnostic secure multiparty computation with perfect security. Traditionally MPC is studied assuming the underlying network is either synchronous or asynchronous. In a network-agnostic setting, the parties are unaware of whether the underlying network is synchronous or asynchronous. The feasibility of perfectly-secure MPC in synchronous and asynchronous networks has been settled a long ago. The landmark work of [Ben-Or, Goldwasser, and Wigderson, STOC'88] shows that $n...

It is well-known that classical Private Information Retrieval (PIR) schemes without preprocessing must suffer from linear server computation per query. Moreover, any such single-server PIR with sublinear bandwidth must rely on public-key cryptography. Several recent works showed that these barriers pertaining to classical PIR can be overcome by introducing a preprocessing phase where each client downloads a small hint that helps it make queries subsequently. Notably, the Piano PIR scheme...

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized...

This paper explores the problem of preventing length leakage in oblivious data access mechanisms with passive persistent adversaries. We show that designing mechanisms that prevent both length leakage and access pattern leakage requires navigating a three-way tradeoff between storage footprint, bandwidth footprint, and the information leaked to the adversary. We establish powerful lower bounds on achievable storage and bandwidth footprints for a variety of leakage profiles, and present...

Doubly Efficient Private Information Retrieval (DEPIR) pertains to a Private Information Retrieval (PIR) scheme with both near-linear server-side preprocessing time and sublinear query time. Very recently, Lin et al. (STOC '23) devised the first single-server DEPIR scheme from standard assumptions. However, their work left one major question open: can we build a DEPIR scheme in the multi-server setting, without relying on heavy cryptographic machinery? In this work, we propose the...

Understanding the fault tolerance of Byzantine Agreement protocols is an important question in distributed computing. While the setting of Byzantine faults has been thoroughly explored in the literature, the (arguably more realistic) omission fault setting is far less studied. In this paper, we revisit the recent work of Loss and Stern who gave the first protocol in the mixed fault model tolerating $t$ Byzantine faults, $s$ send faults, and $r$ receive faults, when $2t+r+s<n$ and omission...

Recent improvements to garbled circuits are mainly focused on reducing their size. The state-of-the-art construction of Rosulek and Roy~(Crypto~2021) requires $1.5\kappa$ bits for garbling AND gates in the free-XOR setting. This is below the previously proven lower bound $2\kappa$ in the linear garbling model of Zahur, Rosulek, and Evans~(Eurocrypt~2015). Recently, Ashur, Hazay, and Satish~(eprint 2024/389) proposed a scheme that requires $4/3\kappa + O(1)$ bits for garbling AND...

Recent improvements to garbled circuits are mainly focused on reducing their size. The state-of-the-art construction of Rosulek and Roy (Crypto 2021) requires $1.5\kappa$ bits for garbling AND gates in the free-XOR setting. This is below the previously proven lower bound $2\kappa$ in the linear garbling model of Zahur, Rosulek, and Evans (Eurocrypt 2015). Whether their construction is optimal in a more inclusive model than the linear garbling model still remains open. This paper begins...

It is well-known that a system of equations becomes easier to solve when it is overdefined. In this work, we study how to overdefine the system of equations to describe the arithmetic oriented (AO) ciphers Friday, Vision, and RAIN, as well as a special system of quadratic equations over $\mathbb F_{2^{\ell}}$ used in the post-quantum signature scheme Biscuit. Our method is inspired by Courtois-Pieprzyk's and Murphy-Robshaw's methods to model AES with overdefined systems of quadratic...

We study selfish mining attacks in longest-chain blockchains like Bitcoin, but where the proof of work is replaced with efficient proof systems -- like proofs of stake or proofs of space -- and consider the problem of computing an optimal selfish mining attack which maximizes expected relative revenue of the adversary, thus minimizing the chain quality. To this end, we propose a novel selfish mining attack that aims to maximize this objective and formally model the attack as a Markov...

Private information retrieval (PIR) is a fundamental cryptographic primitive that allows a user to fetch a database entry without revealing to the server which database entry it learns. PIR becomes non-trivial if the server communication is less than the database size. We show that building (even) very weak forms of single-server PIR protocols, without pre-processing, requires the number of public-key operations to scale linearly in the database size. This holds irrespective of the number of...

The hardness of Kolmogorov complexity is intricately connected to the existence of one-way functions and derandomization. An important and elegant notion is Levin's version of Kolmogorov complexity, \(\mathsf{Kt}\), and its decisional variant, \(\mathsf{MKtP}\). The question whether \(\mathsf{MKtP}\) can be computed in polynomial time is particularly interesting because it is not subject to known technical barriers such as algebrization or natural proofs that would explain the lack of a...

In this paper, we study the problem of lower bounding any given cost function depending on the false positive and false negative probabilities of adversaries against indistinguishability security notions in symmetric-key cryptography. We take the cost model as an input, so that this becomes a purely information-theoretical question. We propose power bounds as an easy-to-use alternative for advantage bounds in the context of indistinguishability with asymmetric cost functions. We show that...

he unique design of the FLIP cipher necessitated a generalization of standard cryptographic criteria for Boolean functions used in stream ciphers, prompting a focus on properties specific to subsets of $\mathbb{F}_2^n$ rather than the entire set. This led to heightened interest in properties related to fixed Hamming weight sets and the corresponding partition of $\mathbb{F}_2^n$ into n+1 such sets. Consequently, the concept of Weightwise Almost Perfectly Balanced (WAPB) functions emerged,...

The conditional disclosure of secrets (CDS) primitive is among the simplest cryptographic settings in which to study the relationship between communication, randomness, and security. CDS involves two parties, Alice and Bob, who do not communicate but who wish to reveal a secret $z$ to a referee if and only if a Boolean function $f$ has $f(x,y)=1$. Alice knows $x,z$, Bob knows $y$, and the referee knows $x,y$. Recently, a quantum analogue of this primitive called CDQS was defined and related...

We have investigated both the padding scheme and the applicability of algebraic attacks to both XHash8 and XHash12. The only vulnerability of the padding scheme we can find is plausibly applicable only in the multi-rate setting---for which the authors make no claim---and is safe otherwise. For algebraic attack relying on the computation and exploitation of a Gröbner basis, our survey of the literature suggests to base a security argument on the complexity of the variable elimination step...

In this work, we study the worst-case to average-case hardness of the Learning with Errors problem (LWE) under an alternative measure of hardness $−$ the maximum success probability achievable by a probabilistic polynomial-time (PPT) algorithm. Previous works by Regev (STOC 2005), Peikert (STOC 2009), and Brakerski, Peikert, Langlois, Regev, Stehle (STOC 2013) give worst-case to average-case reductions from lattice problems to LWE, specifically from the approximate decision variant of the...

Common random string model is a popular model in classical cryptography with many constructions proposed in this model. We study a quantum analogue of this model called the common Haar state model, which was also studied in an independent work by Chen, Coladangelo and Sattath (arXiv 2024). In this model, every party in the cryptographic system receives many copies of one or more i.i.d Haar states. Our main result is the construction of a statistically secure PRSG with: (a) the output...

Recent improvements to garbled circuits are mainly focused on reducing their size. The state-of-the-art construction of Rosulek and Roy (Crypto 2021) requires $1.5\kappa$ bits for garbling AND gates in the free-XOR setting. This is below the previously proven lower bound $2\kappa$ in the linear garbling model of Zahur, Rosulek, and Evans (Eurocrypt 2015). Recently, Ashur, Hazay, and Satish (eprint 2024/389) proposed a scheme that requires $4/3\kappa + O(1)$ bits for garbling AND...

Evolving secret-sharing schemes, defined by Komargodski, Naor, and Yogev [TCC 2016B, IEEE Trans. on Info. Theory 2018], are secret-sharing schemes in which there is no a-priory bound on the number of parties. In such schemes, parties arrive one by one; when a party arrives, the dealer gives it a share and cannot update this share in later stages. The requirement is that some predefined sets (called authorized sets) should be able to reconstruct the secret, while other sets should learn no...

In the linear garbling model introduced by Zahur, Rosulek, and Evans (Eurocrypt 2015), garbling an AND gate requires at least \(2\kappa\) bits of ciphertext, where $\kappa$ is the security parameter. Though subsequent works, including those by Rosulek and Roy (Crypto 2021) and Acharya et al. (ACNS 2023), have advanced beyond these linear constraints, a more comprehensive design framework is yet to be developed. Our work offers a novel, unified, and arguably simple perspective on garbled...

Sponge hashing is a widely used class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a digest by once again iterating the block function on the final output bits. While much is known about the post-quantum security of...

Garbling schemes are one of the most fundamental objects in cryptography and have been studied extensively due to their broad applicability. The state-of-the-art is a construction in which XOR gates are free and AND gates require $3\kappa/2+\mathcal{O}(1)$ bits per gate, due to Rosulek and Roy (CRYPTO'21). An important technique in their garbling is slicing, which partitions the labels into two equal-length slices. In this paper, we explore the feasibility of the slicing technique for...

One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2010). In this problem, we aim to track the number of events that occur over time, while hiding the existence of every single event. More specifically, in every time step $t\in[T]$ we learn (in an online fashion) that $\Delta_t\geq 0$ new events have occurred, and must respond with an estimate $n_t\approx\sum_{j=1}^t...

The (parallel) classical black pebbling game is a helpful abstraction which allows us to analyze the resources (time, space, space-time, cumulative space) necessary to evaluate a function $f$ with a static data-dependency graph $G$ on a (parallel) computer. In particular, the parallel black pebbling game has been used as a tool to quantify the (in)security of Data-Independent Memory-Hard Functions (iMHFs). However, the classical black pebbling game is not suitable to analyze the cost of...

We study single-server private information retrieval (PIR) where a client wishes to privately retrieve the $x$-th entry from a database held by a server without revealing the index $x$. In our work, we focus on PIR with client pre-processing where the client may compute hints during an offline phase. The hints are then leveraged during queries to obtain sub-linear online time. We present Plinko that is the first single-server PIR with client pre-processing that obtains optimal trade-offs...

Memory-hard functions (MHF) are functions whose evaluation provably requires a lot of memory. While MHFs are an unkeyed primitive, it is natural to consider the notion of trapdoor MHFs (TMHFs). A TMHF is like an MHF, but when sampling the public parameters one also samples a trapdoor which allows evaluating the function much cheaper. Biryukov and Perrin (Asiacrypt'17) were the first to consider TMHFs and put forth a candidate TMHF construction called Diodon that is based on the Scrypt MHF...

This paper focuses on the cryptanalysis of the ASCON family using automatic tools. We analyze two different problems with the goal to obtain new modelings, both simpler and less computationally heavy than previous works (all our models require only a small amount of code and run on regular desktop computers). The first problem is the search for Meet-in-the-middle attacks on reduced-round ASCON-Hash. Starting from the MILP modeling of Qin et al. (EUROCRYPT 2023 & ePrint 2023), we rephrase...

Randomized Partial Checking (RPC} was proposed by Jakobsson, Juels, and Rivest and attracted attention as an efficient method of verifying the correctness of the mixing process in numerous applied scenarios. In fact, RPC is a building block for many electronic voting schemes, including Prêt à Voter, Civitas, Scantegrity II as well as voting-systems used in real-world elections (e.g., in Australia). Mixing is also used in anonymous transfers of cryptocurrencies. It turned out, however,...

This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the lower bounds of variants of the discrete logarithm (DL) problem: the multiple-instance DL and one-more DL problems (and their mixture). We also re-prove the unknown-order GGM lower bounds, such as the order finding, root extraction, and repeated squaring. -...

Previous studies on deep-learning-based side-channel attacks (DL-SCAs) have shown that traditional performance evaluation metrics commonly used in DL, like accuracy and F1 score, are not effective in evaluating DL-SCA performance. Therefore, some previous studies have proposed new alternative metrics for evaluating the performance of DL-SCAs. Notably, perceived information (PI) and effective perceived information (EPI) are major metrics based on information theory. While it has been...

We study the complexity of memory checkers with computational security and prove the first general tight lower bound. Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS '91, Algorithmica '94), allow a user to store and maintain a large memory on a remote and unreliable server by using small trusted local storage. The user can issue instructions to the server and after every instruction, obtain either the correct value or a failure (but not...

The BGV scheme is one of the most popular FHE schemes for computing homomorphic integer arithmetic. The bootstrapping technique of BGV is necessary to evaluate arbitrarily deep circuits homomorphically. However, the BGV bootstrapping performs poorly for large plaintext prime $p$ due to its digit removal procedure exhibiting a computational complexity of at least $O(\sqrt{p})$. In this paper, we propose optimizations for the digit removal procedure with large $p$ by leveraging the properties...

In a seminal work, Ishai et al. (FOCS–2006) studied the viability of designing unconditionally secure protocols for key agreement and secure multi-party computation (MPC) using an anonymous bulletin board (ABB) as a building block. While their results establish the feasibility of key agreement and honest-majority MPC in the ABB model, the optimality of protocols with respect to their round and communication complexity is not studied. This paper enriches this study of unconditional security...

Recently, researchers have proposed many LWE estimators, such as lattice-estimator (Albrecht et al, Asiacrypt 2017) and leaky-LWE-Estimator (Dachman-Soled et al, Crypto 2020), while the latter has already been used in estimating the security level of Kyber and Dilithium using only BKZ. However, we prove in this paper that solving LWE by combining a lattice reduction step (by LLL or BKZ) and a target vector searching step (by enumeration or sieving), which we call a Two-step mode, is more...

When designing filter functions in Linear Feedback Shift Registers (LFSR) based stream ciphers, algebraic criteria of Boolean functions such as the Algebraic Immunity (AI) become key characteristics because they guarantee the security of ciphers against the powerful algebraic attacks. In this article, we investigate a generalization of the algebraic attacks proposed by Courtois and Meier on filtered LFSR twenty years ago. We consider how the standard algebraic attack can be generalized...

Garbling schemes allow to garble a circuit $C$ and an input $x$ such that $C(x)$ can be computed while hiding both $C$ and $x$. In the context of adaptive security, an adversary specifies the input to the circuit after seeing the garbled circuit, so that one can pre-process the garbling of $C$ and later only garble the input $x$ in the online phase. Since the online phase may be time-critical, it is an interesting question how much information needs to be transmitted in this phase and...

Collateral is an item of value serving as security for the repayment of a loan. In blockchain-based loans, cryptocurrencies serve as the collateral. The high volatility of cryptocurrencies implies a serious barrier of entry with a common practice that collateral values equal multiple times the value of the loan. As assets serving as collateral are locked, this requirement prevents many candidates from obtaining loans. In this paper, we aim to make loans more accessible by offering loans with...

A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. $\textsf{Avoid}$) and the remote point problem (abbrev. $\textsf{RPP}$). The upper and lower bounds for these meta problems provide a unified perspective on the complexity of specific explicit construction problems that were previously studied independently. An interesting question largely...

Common block ciphers like AES specified by the NIST or KASUMI (A5/3) of GSM are extensively utilized by billions of individuals globally to protect their privacy and maintain confidentiality in daily communications. However, these ciphers lack comprehensive security proofs against the vast majority of known attacks. Currently, security proofs are limited to differential and linear attacks for both AES and KASUMI. For instance, the consensus on the security of AES is not based on formal...

Dynamic vector commitments that enable local updates of opening proofs have applications ranging from verifiable databases with membership changes to stateless clients on blockchains. In these applications, each user maintains a relevant subset of the committed messages and the corresponding opening proofs with the goal of ensuring a succinct global state. When the messages are updated, users are given some global update information and update their opening proofs to match the new vector...

We consider the mainstream model in secure computation known as the bare PKI setup, also as the {bulletin-board PKI}. It allows players to broadcast once and non-interactively before they receive their inputs and start the execution. A bulletin-board PKI is essentially the minimum setup known so far to implement the model known as {messages-authentication}, i.e., when $P$ is forwarded a signed message, it considers it to be issued by $R$ if and only if $R$ signed it. It is known since...

Regular access to unpredictable and bias-resistant randomness is important for applications such as blockchains, voting, and secure distributed computing. Distributed random beacon protocols address this need by distributing trust across multiple nodes, with the majority of them assumed to be honest. Numerous applications across the blockchain space have led to the proposal of several distributed random beacon protocols, with some already implemented. However, many current random beacon...

Private Simultaneous Messages (PSM) is a minimal model of secure computation, where the input players with shared randomness send messages to the output player simultaneously and only once. In this field, finding upper and lower bounds on communication complexity of PSM protocols is important, and in particular, identifying the optimal one where the upper and lower bounds coincide is the ultimate goal. However, up until now, functions for which the optimal communication complexity has been...

Security proofs of symmetric-key primitives typically consider an idealized world with access to a (uniformly) random function. The starting point of our work is the observation that such an ideal world can lead to underestimating the actual security of certain primitives. As a demonstrating example, $\mathsf{XoP2}$, which relies on two independent random permutations, has been proven to exhibit superior concrete security compared to $\mathsf{XoP}$, which employs a single permutation with...

Weightwise degree-d functions are Boolean functions that take the values of a function of degree at most d on each set of fixed Hamming weight. The class of weightwise affine functions encompasses both the symmetric functions and the Hidden Weight Bit Function (HWBF). The good cryptographic properties of the HWBF, except for the nonlinearity, motivates to investigate a larger class with functions that share the good properties and have a better nonlinearity. Additionally, the homomorphic...

Suppose a prover, in possession of a large body of valuable evidence, wants to quickly convince a verifier by presenting only a small portion of the evidence. We define an Approximate Lower Bound Argument, or ALBA, which allows the prover to do just that: to succinctly prove knowledge of a large number of elements satisfying a predicate (or, more generally, elements of a sufficient total weight when a predicate is generalized to a weight function). The argument is approximate because...

In secure multiparty computation (MPC), the goal is to allow a set of mutually distrustful parties to compute some function of their private inputs in a way that preserves security properties, even in the face of adversarial behavior by some of the parties. However, classical security definitions do not pose any privacy restrictions on the view of honest parties. Thus, if an attacker adversarially leaks private information to honest parties, it does not count as a violation of privacy. This...

The Unitary Synthesis Problem (Aaronson-Kuperberg 2007) asks whether any $n$-qubit unitary $U$ can be implemented by an efficient quantum algorithm $A$ augmented with an oracle that computes an arbitrary Boolean function $f$. In other words, can the task of implementing any unitary be efficiently reduced to the task of implementing any Boolean function? In this work, we prove a one-query lower bound for unitary synthesis. We show that there exist unitaries $U$ such that no...

We present new lower and upper bounds on the number of communication rounds required for asynchronous Crusader Agreement (CA) and Binding Crusader Agreement (BCA), two primitives that are used for solving binary consensus. We show results for the information theoretic and authenticated settings. In doing so, we present a generic model for proving round complexity lower bounds in the asynchronous setting. In some settings, our attempts to prove lower bounds on round complexity fail....

Given two linear codes, the code equivalence problem asks to find an isometry mapping one code into the other. The problem can be described in terms of group actions and, as such, finds a natural application in signatures derived from a Zero-Knowledge Proof system. A recent paper, presented at Asiacrypt 2023, showed how a proof of equivalence can be significantly compressed by describing how the isometry acts only on an information set. Still, the resulting signatures are far from being...

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that, assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of works follow-up the result of Garg et al. matching this lower bound under a...

In 2022, Moriya, Onuki, Aikawa, and Takagi proposed a new framework named generalized Montgomery coordinates to treat one-coordinate type formulas to compute isogenies. This framework generalizes some already known one-coordinate type formulas of elliptic curves. Their result shows that a formula to compute image points under isogenies is unique in the framework of generalized Montogmery coordinates; however, a formula to compute image curves is not unique. Therefore, we have a question:...

Anonymous transfer, recently introduced by Agrikola, Couteau and Maier [ACM22] (TCC '22), allows a sender to leak a message anonymously by participating in a public non-anonymous discussion where everyone knows who said what. This opens up the intriguing possibility of using cryptography to ensure strong anonymity guarantees in a seemingly non-anonymous environment. The work of [ACM22] presented a lower bound on anonymous transfer, ruling out constructions with strong anonymity guarantees...

An hard homogeneous space (HHS) is a finite group acting on a set with the group action being hard to invert and the set lacking any algebraic structure. As such HHS could potentially replace finite groups where the discrete logarithm is hard for building cryptographic primitives and protocols in a post-quantum world. Threshold HHS-based primitives typically require parties to compute the group action of a secret-shared input on a public set element. On one hand this could be done...

Sponge paradigm, used in the design of SHA-3, is an alternative hashing technique to the popular Merkle-Damgård paradigm. We revisit the problem of finding $B$-block-long collisions in sponge hash functions in the auxiliary-input random permutation model, in which an attacker gets a piece of $S$-bit advice about the random permutation and makes $T$ (forward or inverse) oracle queries to the random permutation. Recently, significant progress has been made in the Merkle-Damgård setting and...

In 2018, Aono et al. (ASIACRYPT 2018) proposed to use quantum backtracking algorithms (Montanaro, TOC 2018; Ambainis and Kokainis, STOC 2017) to speedup lattice point enumeration. Quantum lattice sieving algorithms had already been proposed (Laarhoven et al., PQCRYPTO 2013), being shown to provide an asymptotic speedup over classical counterparts, but also to lose competitiveness at dimensions relevant to cryptography if practical considerations on quantum computer architecture were taken...

A major open problem in information-theoretic cryptography is to obtain a super-polynomial lower bound for the communication complexity of basic cryptographic tasks. This question is wide open even for very powerful non-interactive primitives such as private information retrieval (or locally-decodable codes), general secret sharing schemes, conditional disclosure of secrets, and fully-decomposable randomized encoding (or garbling schemes). In fact, for all these primitives we do not even...

Correlation intractability is an emerging cryptographic paradigm that enabled several recent breakthroughs in establishing soundness of the Fiat-Shamir transform and, consequently, basing non-interactive zero-knowledge proofs and succinct arguments on standard cryptographic assumptions. In a nutshell, a hash family is said to be \emph{correlation intractable} for a class of relations $\mathcal{R}$ if, for any relation $R\in\mathcal{R}$, it is hard given a random hash function $h\gets H$ to...

Motivated by the extended deployment of authenticated data structures (e.g., Merkle Patricia Tries) for verifying massive amounts of data in blockchain systems, we begin a systematic study of the I/O efficiency of such systems. We first explore the fundamental limitations of memory checking, a previously-proposed abstraction for verifiable storage, in terms of its locality---a complexity measure that we introduce for the first time and is defined as the number of non-contiguous memory...

Constructing key-agreement protocols in the random oracle model (ROM) is a viable method to assess the feasibility of developing public-key cryptography within Minicrypt. Unfortunately, as shown by Impagliazzo and Rudich (STOC 1989) and Barak and Mahmoody (Crypto 2009), such protocols can only guarantee limited security: any $\ell$-query protocol can be attacked by an $O(\ell^2)$-query adversary. This quadratic gap matches the key-agreement protocol proposed by Merkle (CACM 78), known as ...

Broadcast protocols enable a set of $n$ parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most...

This work formally analyzes the anonymity guarantees of continuous stop-and-go mixnets and attempts to answer the above question. Existing mixnet based anonymous communication protocols that aim to provide provable anonymity guarantees rely on round-based communication models --- which requires synchronization among all the nodes and clients, and difficult to achieve in practice. Continuous stop-and-go mixnets (e.g., Loopix and Nym) provide a nice alternative by adding a random delay for...

BGV and BFV are among the most widely used fully homomorphic encryption (FHE) schemes. Both schemes have a common plaintext space, with a rich algebraic structure. Our main contribution is to show how this structure can be exploited to more efficiently homomorphically evaluate polynomials. Namely, using Galois automorphisms, we present an algorithm to homomorphically evaluate a polynomial of degree $d$ in only $3\log(d)$ (in some cases only $2\log(d)$) many ciphertext-ciphertext...

Interactive oracle proofs (IOPs) (Ben-Sasson et al., TCC 2016; Reingold et al., SICOMP 2021) have emerged as a powerful model for proof systems combining IP and PCP. While IOPs are not any more powerful than PCPs from a complexity theory perspective, their potential to create succinct proofs and arguments has been demonstrated by many recent constructions achieving better parameters such as total proof length, alphabet size, and query complexity. In this work, we establish new results on the...

Correlated secret randomness is a useful resource for secure computation protocols, often enabling dramatic speedups compared to protocols in the plain model. This has motivated a line of work on identifying and securely generating useful correlations. Different kinds of correlations can vary greatly in terms of usefulness and ease of generation. While there has been major progress on efficiently generating oblivious transfer (OT) correlations, other useful kinds of correlations are...

The paper extends Shannon's classical theory of ciphers. Here ciphers are modeled by Latin rectangles and their resistance to brute force attack is assessed through the valence of cryptograms. The valence of a cryptogram is defined as the number of all meaningful messages produced by decrypting the cryptogram with all possible keys. In this paper, the mean cryptogram valence of an arbitrary modern cipher with K keys, N outputs and N inputs, of which M inputs are messages, is derived....

Time-Lock puzzles (TLP) are cryptographic protocols that enable a client to lock a message in such a way that a server can only unlock it after a specific time period. However, existing TLPs have certain limitations: (i) they assume that both the client and server always possess sufficient computational resources and (ii) they solely focus on the lower time bound for finding a solution, disregarding the upper bound that guarantees a regular server can find a solution within a certain time...